---
title: "A simple pendulum of length \\(L\\) is released from rest at a small angle \\(\\theta_0\\). A thin horizontal peg is located at a distance \\(d\\) directly below the pivot point, where \\(d < L\\). As the bob swings through its lowest point, the string strikes the peg, causing the bob to swing the remainder of its arc with a shorter effective length. Which of the following is a correct expression for the total time required for the bob to complete one full oscillation?"
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url: "https://nerd-notes.com/ubq/113092/"
date_modified: "2026-05-05T03:46:25+00:00"
---

# A simple pendulum of length \(L\) is released from rest at a small angle \(\theta_0\). A thin horizontal peg is located at a distance \(d\) directly below the pivot point, where \(d < L\). As the bob swings through its lowest point, the string strikes the peg, causing the bob to swing the remainder of its arc with a shorter effective length. Which of the following is a correct expression for the total time required for the bob to complete one full oscillation?

A simple pendulum of length \(L\) is released from rest at a small angle \(\theta_0\). A thin horizontal peg is located at a distance \(d\) directly below the pivot point, where \(d < L\). As the bob swings through its lowest point, the string strikes the peg, causing the bob to swing the remainder of its arc with a shorter effective length. Which of the following is a correct expression for the total time required for the bob to complete one full oscillation?

![A ceiling with a pivot point is shown. A string of length L hangs from the pivot to a mass m. A small circular peg is fixed on the vertical line at a distance d below the pivot. The bob is shown at its release position to the left, at a small angle theta relative to the vertical. A dashed line indicates the bob's trajectory and the vertical center line through the pivot and peg.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777952785-AAtKkP.jpg)

- **A.** \(\pi \left( \sqrt{\dfrac{L}{g}} + \sqrt{\dfrac{L-d}{g}} \right)\)
- **B.** \(2\pi \left( \sqrt{\dfrac{L}{g}} + \sqrt{\dfrac{L-d}{g}} \right)\)
- **C.** \(\pi \left( \sqrt{\dfrac{L}{g}} + \sqrt{\dfrac{d}{g}} \right)\)
- **D.** \(\pi \sqrt{\dfrac{2L-d}{g}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113092/*